The German Ölberg is a gravely wrong translation of the Greek name for the Mount of Olives ὄρος τῶν ἐλαιῶν (oros ton elaion). The Greek version is absolutely unambiguous when spoken, or written with accents. An ambiguity arises when using capital letters, as these don't allow for the placement of accents. The small-letter Greek writing system was finalised roughly in the 9th century, hence old Christian writings are bound to use capital letters. Accents where invented before the second century before common era, but not used mandatorily. Still, a native speaker, who had lived in the Mediterranean, could never succumb to such confusion.
When written without accents ΕΛΑΙΩΝ is genitive plural of two lemmata, ἐλαία and ἔλαιον - thus it means both “of olives” and “of oils”. Accents are crucial to all varieties of Greek, old or modern, but are usually omitted in the old, capitalised form of writing.
In the tables above one of the lemmata bears the circumflex accent, called περισπωμένη in Greek! Hence they are clearly different. Perhaps Luther did not notice that, or his Greek was not very good. As the latter seems unlikely, another unlikely theory would be, that he used text in capital letters.
A translation similar to the German is used in Danish, Slovene and Finnish. Bulgarian and Russian simply use a cognate of the Greek word elaion. Most other languages – including Latin, its descendants and English – apparently took the other interpretation or translated directly from Hebrew.
Note that in many languages, words for “oil” (in the culinary sense especially) and “olive” have the same root.
Arabic: زيتون / زيت (zayt / zaytun)
Greek: έλαιο / ελιά
Spanish: aceite / aceituna (from Arabic)
Latin: oleum / olea (from Greek)
Maltese: żejt / żebbuġ
Serbo-Croatian, Bulgarian: maslo / maslina
So they are very intertwined concepts in the Mediterranean.
Likewise the various Germanic cognates of “oil” are from Latin oleum (“olive oil”), from Ancient Greek ἔλαιον (élaion, “olive oil”).
Later German, English and other languages lost the association of “oil” with olives, or perhaps the association was never so strong - north of the Alps, olives were very exotic in the past, and oil was associated with animal fats not plant fats.
Während bei den Griechen und Römern das Olivenöl bereits in der Antike zum Braten und Verfeinern von Speisen üblich und die Butter nur für medizinische Zwecke eingesetzt wurde, dominierten in der deutschen Küche Butter, Schmalz und Fette noch bis ins frühe 20. Jahrhundert. In einem Bericht über die erste Fischereiausstellung in Wien (September 1902) beschreibt die Zeitschrift Die Woche vor allem französische Fischrezepte mit Olivenöl und klagt über die Speisefett-Versessenheit Zentraleuropas.
See: ἐλαία, ἔλαιον, زيت, זית
The reconstructed proto-Germanic word for grease is smerwą, which yielded German Schmer, English smear and Yiddish שמיר.
Common words for the oil that one should never ever eat in Russian, Turkish, Hebrew, Arabic etc derive from the Old Persian word نفت (naft), cognate with the German scientific term Naphtha a.k.a. Rohbenzin. In fact the etymology of Benzin is also Arabic and interesting.
But nobody is calling the Mount of Olives Schmerhaufen or Benzinspitz.